What is 3/39 plus 3/13? (Answer: 4/13)

Exact Answer

==================================================
Problem: What is 3/39 plus 3/13?
Formula / Expression: 3/39 + 3/13
Final Answer: 4/13
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.
Working: LCD(39, 13) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 3/39 by 1, and multiply the numerator and denominator of 3/13 by 3 so both fractions share the common base 39.
Working: 3 × 1/39 × 1 = 3/39 and 3 × 3/13 × 3 = 9/39

Step 3: Add the Numerators
Now add the numerators (3 + 9 = 12) and keep the common denominator 39 unchanged.
Working: 3 + 9/39 = 12/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 12 ÷ 3/39 ÷ 3 = 4/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).
Working: 4 ÷ 13 = 0.307692 (30.7692%)

Key Values:
- Simplified Fraction: 4/13
- Mixed Number Form: 4/13
- Decimal Value: 0.307692
- Percentage: 30.7692%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-39-plus-3-13/
==================================================

3/39 + 3/13 = 4/13

Simplified Fraction

4/13

Mixed Number

Proper (4/13)

Decimal Value

0.307692

Percentage

30.7692%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 3/39 + 3/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.

LCD(39, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 3/39 by 1, and multiply the numerator and denominator of 3/13 by 3 so both fractions share the common base 39.

3 × 1/39 × 1 = 3/39 and 3 × 3/13 × 3 = 9/39

Step 3

Add the Numerators

Now add the numerators (3 + 9 = 12) and keep the common denominator 39 unchanged.

3 + 9/39 = 12/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 39, which is 3. Divide both the numerator and denominator by 3.

12 ÷ 3/39 ÷ 3 = 4/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).

4 ÷ 13 = 0.307692 (30.7692%)

Visual Representation

The diagram below illustrates 3/39 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/13`
Mixed Number Form	`4/13`
Decimal Form	`0.307692`
Percentage	`30.7692%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/39 plus 3/13 as a fraction?

3/39 + 3/13 in simplest fraction form is 4/13.

What is 3/39 plus 3/13 as a decimal?

3/39 + 3/13 converted to a decimal is 0.307692.

What is 3/39 plus 3/13 as a percentage?

3/39 + 3/13 expressed as a percentage is 30.7692%.

Does 3/39 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.307692...) because the denominator contains prime factors other than 2 and 5.